Right before chicks hatch, they have just absorbed the last of the yolk. This sustains them during their journey, for up to three days, so that's why they need to ship at that time, when the yolk will sustain them.
The reason nature works this way is that if they were hatching beneath a mother hen, this would enable the early hatchers to survive without eating and drinking until mother finished hatching the rest of the eggs. She can't get up from the nest until the entire hatching is over, or else the last babies would die in their shells, unable to hatch without their mother's warmth. It's for this reason that shipping chicks that are more than one day old is unsafe, because after that, the babies don't have the stores needed to survive the journey.